When real-life 1950s greasers were often from the "wrong side of the tracks" and unlikely to mix with middle-class kids?

Yes to what you mentioned. They really WERE unlikely to mix, and Ritchie's father constantly mentions that in S1 (especially "Fonzie Drops In", IIRC).

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Joanie speaks what is on everyone's mind, as usual!:)

Eventually the Cunninghams begins to trust Fonzie...sometime around "The Best Man", when Fonzie helps the wedding. And their trust rises to 100% in mid-Season 2 when they invite him for Christmas. But given that he looks and acts like a criminal, this is a leap of faith on the Cunninghams' part.

Also worth mentioning that "wrong side of the tracks" generally denotes that the person is living in a segregated area for those of lesser income, which tends to be BIPOC for systemic reasons. And this divide is especially common in Milwaukee which was and still is heavily segregated. (https://en.wikipedia.org/wiki/Milwaukee#:~:text=it%20continues%20to%20be%20one%20of%20the%20most%20racially%20segregated%20cities%20as%20a%20result%20of%20early%2D20th%20century%20redlining.%5B13%5D)
So, the choice to make him a white Italian is quite an interesting choice as well...

I'd argue specifically BECAUSE he is the "no good" "bad boy" , he seems to attract the viewers' and writers' attention . If you watch the first half of S1 you'll see he just doesn't say or do much, but the mystery of his dropout character captures the imagination.

So, this happened for the same reason that people are really into Disney villains, or why the bullies from many Nickelodeon cartoons (like Arthur's Binkie or Arnold's Harold Berman) went from antagonists to eventual friends of the protagonists. (Nelson from The Simpsons, less so.)